Last Updated：2025/11/21

Dictionary quizzes to help you remember the meaning

Dictionary quizzes to help you remember the meaning

supremum

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Source Word

supremum

(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.

Japanese Meaning

数学において、集合Xの全要素以上である実数の中で最も小さいもの、すなわち最小上界（上限）を指す。 / 順序理論では、部分順序集合Pにおいて集合Xのすべての要素以上となる要素の中で最小のものを意味する。

What is this buttons?

For the set {1 - 1/n : n ∈ N}, the supremum is 1, even though 1 is not an element of the set.

Google Translation / DeepL Translation

集合 {1 - 1/n : n ∈ N} に対して、最小上界は 1 ですが、1 はその集合の要素ではありません。

Sense（1）

(set theory) (real analysis): Given a subset X of R, the smallest real number that is ≥ every element of X; (order theory): given a subset X of a partially ordered set P (with partial order ≤), the least element y of P such that every element of X is ≤ y.

A sublattice of a lattice is a subset that is closed under pairwise infima and suprema.

Google Translation / DeepL Translation

suprema

（ plural ）

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